Energy of electron-hole pairs in 3D space

[Jeffrey Yang]

Dear All:

I'm trying to use fluctuation dissipation theorem to describe spontaneous photon emission process by electron-hole recombination in semiconductor material.

I notice that all the references using such a method considers the dipole's degree of freedom separately, for example in x, y, z direction separately, and then sum together. Does this means that the actual total energy of the oscillator in 3D space is 3ħω? But for after the emission of one electron-hole pair the photon's energy is just ħω. How to understand this?

 

[eljose79]

Thank you for your question about the use of the fluctuation dissipation theorem in describing spontaneous photon emission by electron-hole recombination in semiconductor materials. The fluctuation dissipation theorem is a powerful tool in understanding the behavior of physical systems, and it is often used in the study of semiconductors.

To answer your question, it is important to first understand the concept of degrees of freedom in a physical system. In this case, the degrees of freedom refer to the different ways in which energy can be stored or distributed in the system. In the case of a dipole oscillator, the energy can be stored in three different directions, hence the three degrees of freedom.

When we consider the total energy of the oscillator in 3D space, we are taking into account all three degrees of freedom. This means that the energy can be distributed among the three directions, with each direction contributing a certain amount to the total energy. In the case of the emission of a photon, the energy is only released in one direction, resulting in a photon with energy ħω.

In essence, the total energy of the oscillator in 3D space is not always equal to the energy of the emitted photon. This is because the energy is distributed among the different degrees of freedom in the system. The use of the fluctuation dissipation theorem takes this into account and allows us to accurately describe the behavior of the system.

I hope this helps to clarify your understanding of the use of the fluctuation dissipation theorem in this context. If you have any further questions, please feel free to ask. As scientists, it is important for us to continue learning and exploring new ideas and concepts. Best of luck with your research.